This guy is a fool if he thinks that. The Roman upper classes admired the Greeks, all educated Romans learned Greek, and a Roman like Pontius Pilate would have studied Greek extensively and spoken it among his educated friends (much as young men in the British Empire used to sling Latin around - only more so.)
It is clear from the classical writers that slaves, gladiators, and soldiers spoke a Vulgar Latin that was the ancestor of the Romance languages (as the legionaries spread around the Empire, were given land, and settled.) Suetonius and Martial, among others, mention it. Think of the difference today between the language of a highly educated university professor and some teenage skateboarding dude on the street corner.